I have a couple of rifles which will digest Rem, and Win brass loads close enough to the same POI out to 400yds that the differences could only be told using a mechanical rest to hold the rifle.
However, when I worked these loads up, I worked them up individually in both case brands to be sure things were going to work out with pressure issues and accuracy. I have been very fortunate that these particular rifles have shot just about everything I have tried through them with little issue. The loads aren't always top end loads, but a couple have been and they worked fine for my uses.
Your milage may vary, and your ranges might be much further than what I push these rifles to. Either way as was mentioned, it is nice to know one way or the other. Even if one brand has a slightly different charge weight, it might still shoot right along side the other. so you could still utilize the different cases. With my .270 Win, I simply load and shoot both Rem, and Win case identical with the load I worked up. However is I use Federal or Hornady cases, I have to back down around a full grain to keep things working properly. I simply use the latter for practice and in the woods hunting. They use completely different bullets and out to 200yds, with them I don't have to change anything sight wise. They are primiarly for hogs and shots are generally between 10' and 50yds. Howeve rthey do work on out a ways, if needed. The standard loads are top end in Win and Rem cases and have been verified out to 600yds, which for the stock Rem BDL is about as far as I would ever push it. The scope is a Burris with the Ballistic Plex and the loads correspond to each hash mark on the retical. It makes shots on deer out to 300 very easily accomplished and for the further ranged hogs, simply a chip shot given the proper conditions.
Good luck and don't hesitate to try the other cases. The one thing which might surprise you is you could actually get better groups from the other brands.